For the most part, punctuation will go inside quotation marks. There. I wanted to get that out of the way. If you need punctuation at the end of a quotation (and check guide above to see whether or not you do), and you are writing according to MLA standards, your punctuation will be in the correct spot most of the time if you keep the punctuation marks inside the quotation marks (in other words: between the last letter of the quotation and the closing quotation mark).
Sometimes, this is what we have to do when quoting a text that doesn't have page numbers. Since we can't cite a page number, then we can't use parenthetical citations (like we would with a book, shown in the example above). Here's how that might look:
According to Malcolm Gladwell's "The Courthouse Ring: Atticus Finch and the Limits of Southern Liberalism," "If Finch were a civil-rights hero, he would be brimming with rage at the unjust verdict."
Notice the period between the t in "verdict," and the closing quotation mark. Gladwell ends his sentence just that way too, so the period was taken directly from the article, and included as it appears in the text. All we did to quote it is add quotation marks at the beginning and the end, making sure that the closing period appears immediately after the period.
You may also notice the comma after the word "Liberalism" in the article's title. Keep in mind that article titles should be noted with quotation marks in MLA standards, so the same rules apply here for punctuation: we need a comma before the quotation begins, but since the last word right before the quotation is part of the article title, we need to make sure that the comma appears inside those quotation marks too (even though there would be no comma at the end of the title if we pulled up the website).
Sometimes, we might quote only part of a sentence, so the quotation would normally end with a comma or other punctuation mark. In that case, we actually change the punctuation mark from what we see in the quotation. So, something like this:
Describing Atticus' decision at the end of the novel, Gladwell explains, "Boo Radley, the reclusive neighbor of the Finches, comes to the children’s defense, and in the scuffle Radley kills Ewell. Sheriff Tate brings the news to Finch, and persuades him to lie about what actually happened;"
Would be changed to:
Describing Atticus' decision at the end of the novel, Gladwell explains, "Boo Radley, the reclusive neighbor of the Finches, comes to the children’s defense, and in the scuffle Radley kills Ewell. Sheriff Tate brings the news to Finch, and persuades him to lie about what actually happened."
Even though the original text does not end the sentence there, it's fine to make small edits to a quotation to make the quotation fit your sentence better (as long as you're not changing the meaning of the quotation). There's no change in meaning to the sentence if we change a comma or a semicolon to a period, so it's fine to make these changes to a quotation. Just remember to keep the punctuation (if it should be there) inside the quotation marks.